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Demonstrate freedom of detecting disease?

It is impossible to prove that a population is free from a particular disease without testing every individual with a perfect test. However, demonstrating "freedom" from disease in a population is essentially the same as sampling to provide a high level of confidence of detecting disease at specified (design) prevalence. If we don't detect disease, then we can state that we have the appropriate level of confidence that (if the disease is present) it is at prevalence lower than the design prevalence. Provided we have selected appropriate design prevalence, it can then be argued that if the disease were present it would more than likely be at a higher level than the design prevalence, and therefore we can be confident that the population is probably free of the disease.